Master equation analysis of intermolecular energy transfer in multiple-well, multiple-channel unimolecular reactions. I. Basic theory

Prasana K. Venkatesh, Anthony M. Dean, Morrel H. Cohen, Robert W. Carr

Research output: Contribution to journalArticle

29 Scopus citations

Abstract

We present a full theoretical analysis of the master-equation formulation of the problem of intermolecular energy transfer in multiple-well, multiple-channel systems. It is shown that the master equation for chemical or thermal activation possesses a unique steady state, that corresponding to the trivial solution. Rate equations local in time and therefore time-independent rate coefficients for the dissociating processes may be obtained only if a state of secular equilibrium exists. For chemically-activated systems, a general state of secular equilibrium may exist which may contain within it a regime wherein there is a well-separated, nontrivial, least negative eigenvalue of the master equation kernel. The dynamics of thermally activated systems are similarly deduced by treating them as chemically activated systems with appropriate modifications to the inhomogeneous source term of the master equation. A degenerate and nondegenerate perturbation theory analysis of the case of rapid thermalization in the vicinity of the thermodynamic equilibrium state is also enunciated. The special case of negligible thermalization is analyzed. A classification of the ordering of the time scales of thermalization, isomerization, and dissociation is then given.

Original languageEnglish (US)
Pages (from-to)8904-8916
Number of pages13
JournalJournal of Chemical Physics
Volume107
Issue number21
DOIs
StatePublished - Dec 1 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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